Re: Exponential fit question.
- To: mathgroup at smc.vnet.net
- Subject: [mg28025] Re: [mg27986] Exponential fit question.
- From: Chris Johnson <cjohnson at shell.faradic.net>
- Date: Wed, 28 Mar 2001 02:40:57 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
After a few minutes more looking, I don't think your Excel coefficients
are better than Mathematica. This solution appears optimal to me.
Chris
On Tue, 27 Mar 2001, Chris Johnson wrote:
> Joe,
>
> The Fit function only looks for Linear combinations of the functions
> provided. You are looking for a non-linear solution which you can get by
> loading the package Statistics`NonlinearFit`.
>
> After loading the package, it seems the solution is very unstable, so
> mathematica still needs a nudge to push it in the right direction. Here
> is what I found...
>
> In[93]:=
> data = {{50, 22}, {64, 62}, {78, 122}, {93, 269},
> {107, 414}, {122, 507}, {136, 597}};
>
> And just to see what we are working with...
> p1 = ListPlot[data]
>
> First, I wanted to confirm your results...
>
> In[94]:=
> fitcurve = Fit[data, Exp[x], x]
>
> Out[94]=
> 5.151397928273716*^-57*E^x
>
> Which doesn't quite match what Mathematica gave you, but close enough.
> And a plot of this relative to your data show it is not a reasonable fit.
>
> Next I load the NonlinearFit package and use that function...
>
> Needs["Statistics`NonlinearFit`"]
>
> In[95]:=
> g2 = NonlinearFit[data, a1*E^(a2*x), x, {a1, a2}]
>
> Out[95]=
> 4.930380657631324*^-32*E^(1.*x)
>
> This is no good, it assumes the x coeff. to be 1, and a plot of g2 is just
> as bad as the first attempt using Fit. The next step was to give
> Mathematica a nudge in the expected direction by this trick:
>
> In[96]:=
> g3 = NonlinearFit[data, a1*E^(0.001*a2*x), x, {a1, a2}]
>
> Out[96]=
> 26.60851641163635*E^(0.02349567063425155*x)
>
> A plot of g3 relative to the p1 plot shows a pretty close fit.
>
> Still, the parameters you have found with Excel do get closer on a Least
> Squares basis. I hope someone else can help more, but I thought this
> might be a good start.
>
> Chris
>
>
> On Tue, 27 Mar 2001, joe wrote:
>
> > hello.
> >
> > I was wondering if someone could help me with the following problem.
> >
> > I am trying to perform an exponential fit to the following data
> > {{x,y}}
> >
> > data
> > ={{50,22},{64,62},{78,122},{93,269},{107,414},{122,507},{136,597}}
> >
> > Fit[data,Exp[x],x]
> >
> > what I get is
> >
> > 1.94272422061017735^-63 *E^x Which is not correct.
> >
> > With Excel I get 7.5*E^0.0034x which is correct.
> >
> > How can I do this with Mathematica ?
> >
> > Thanks.
> > -Joseph.
> >
> >
>
>